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The electric field in a region is given ...

The electric field in a region is given by `vecE = (A/x^3) vecI.` Write a suitable SI unit for A. Write an experssion for. the potential in the region assuming the potential at. infinity to be zero.

Text Solution

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As `E =(A)/(x^(3)) , A = Ex^(3) = (N//C)m^(3) = Nm^(3) //C`
Potential in the region
`V = - int_(oo)^(x) vec(E).vec(d) x = - int_(oo)^(x) ((A)/(x^(3)) hat(i)) . (dx hat(i))`
` = - A int_(oo)^(x) x^(-3) dx = - A [(x^(-2))/(-2)]_(oo)^(x) = (A)/(2x^(2))`
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